Problem: The mean and median of a set of three numbers is 16, and the smallest number of the three is 5. What is the largest of the three numbers?
Explanation: Let the middle number and largest number be $a$ and $b$ respectively, so that the three numbers are $5$, $a$, and $b$. Since the mean and median of these three numbers are both $16,$ we have \[\frac{5+a+b}{3} = 16\] and \[a = 16.\] Solving for $b$ gives \[5+16+b = 48 \Rightarrow b = \boxed{27}.\]